Aim: How do we find the sine of the difference of two angles and the sine of the sum of two angles? (These formulas will be on the Regents Reference sheet)

By the end of the lesson, you will be able to...
  1. verify the validity of the formula for the sine of the difference of two angles
  2. verify the validity of the formula for the sine of the sum of two angles
  3. apply the formulas for sin(A - B) and sin (A+B) to find the exact value of expressions involving angles measured in radians and in degrees
  4. state the sum and difference formulas in words

Before you begin watching the videos, copy down the following questions into your notebook. Answer them as you watch the video.

  1. What is the sine sum formula?
  2. What is the sine difference formula?
  3. How does the sine sum formula differ from the cosine formula?
  4. How does the sine difference formula differ from the cosine difference formula?


Video 1

Video 2


  • Classwork: Solve each problem using the sine sum or sin difference formulas.

  1. Find the exact value of sin 15 degrees. (Ans: (sqrt6 - sqrt2)/4)
  2. Show that sin (pi + c) = - sin c

  • Homework: Do numbers 3-21 in multiples of 3.

Sine_Sum_and_difference.JPG

  • Answers

A-Sine_sum_and_diff.JPG

  • Journal entry: How can we use the formulas today to derive the formula for sin (A + B + C)?